Entropic uncertainty relations from equiangular tight frames and their applications

Abstract

Finite tight frames are interesting in various respects, including potential applications in quantum information science. Indeed, each complex tight frame leads to a non-orthogonal resolution of the identity in the Hilbert space. In a certain sense, equiangular tight frames are very similar to the maximal sets that provide symmetric informationally complete measurements. Hence, applications of equiangular tight frames in quantum physics deserve more attention than they have obtained. We derive entropic uncertainty relations for a quantum measurement built of the states of an equiangular tight frame. First, the corresponding index of coincidence is estimated from above, whence desired results follow. State-dependent and state-independent formulations are both presented. We also discuss applications of the corresponding measurements to detect entanglement and steerability.

Uncertainty relations for coherence quantifiers based on the Tsallis relative 1/2-entropies

“…As was already mentioned, equiangular tight frames are easier to construct than SIC-POVMs. Related measurements are shown to be useful in detection of entanglement and steerability [42]. The uncertainty relation for the considered quantifier with respect to an ETF-based measurement is formulated below.…”